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Rethinking how we teach mathematics

As an undergraduate student, Krista Bresock never imagined that she would pursue a degree in mathematics. However, after an eye-opening conversation with a teaching assistant during an office hour visit, Bresock decided to take additional math courses and quickly developed a passion for the subject.

Krista Bresock teaching   
Krista Bresock

“I was amazed at what math could be and how much it sparked my interest,” said Bresock, a Grafton, West Virginia, native.

Now a mathematics instructor and Ph.D. student in the West Virginia University Department of Mathematics, Bresock researches student learning of integral calculus and is a teaching instructor, serving as the lead instructor of MATH 156, Calculus 2.

In July 2018, Bresock traveled to Umeå, Sweden, for the 42nd Annual Meeting of the International Group for the Psychology of Mathematics Education, which is one of the largest math conferences in the world, to present her research on calculus students’ visualizations when solving volume problems.

Krista in Sweden
Bresock in Umeå, Sweden

“My research seems to be uncovering the idea that students tend to learn and understand topics in the same way that they are presented,” Bresock said. “For example, if a teacher presents the calculus material in a way that is heavily formulaic and dependent on memorized equations instead of on a foundation of deep understanding of the concepts, students will learn the material on a superficial level and not be able to apply the concepts in different and novel mathematical situations.”

According to Bresock, volume problems are unique because they require proficiency in two important areas of calculus, integration and visualization.

“I kept finding that many students would produce wildly inaccurate pictures, but build a correct integral, or they would sketch a perfect picture, but produce a wildly inaccurate integral,” Bresock said.

Bresock was inspired to conduct this research after several semesters of teaching MATH 156.

“I think math in general, and calculus in particular, are fascinating and beautiful subjects,” Bresock said. “Throw in the fact that I get to talk to so many different, unique, bright, fun students about math, and it just becomes something incredibly enjoyable that feels nothing like a job.”

Krista with Moose in Sweden
Bresock in Umeå, Sweden

After completion of her Ph.D., Bresock hopes to continue working at WVU and continue to teach and further her research.

“Krista is one of our most dedicated instructors in the Department of Mathematics. She skillfully teaches hundreds of students every year. She cares deeply about the students and goes above and beyond her normal teaching duties to help students succeed,” said Marjorie Darrah, chair of the Department of Mathematics. “The fact that she is also doing her graduate studies in our department and focusing on discovering more about how students think about and learn calculus is a wonderful added benefit to the department.”